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 // This example shows how to import discrete experimental data and transform it into // a continuous data range usable in general expressions in sparselizard. // The measured data must first be smoothed externally before being sampled at enough // points to obtain a good interpolation with the cubic splines used in the 'spline' object. // The sampling points should not be placed too close to each other to avoid numerical issues. #include "sparselizardbase.h" using namespace mathop; void sparselizard(void) { // The domain regions as defined in 'disk.geo': int vol = 1, sur = 2, top = 3; // The mesh can be curved! mesh mymesh("disk.msh"); // Nodal shape functions 'h1' with 3 components for the mechanical displacement u [m]. // Field T is the temperature [K] and x/y is the x/y coordinate. field u("h1xyz"), T("h1"), x("x"), y("y"); // Use interpolation order 2 on 'vol', the whole domain: u.setorder(vol, 2); // Clamp on surface 'sur' (i.e. 0 valued-Dirichlet conditions): u.setconstraint(sur); // Load the measured Young's modulus versus temperature data samples in a spline object: spline measureddata("steel-stiffness-temperature.txt"); // Define the expression giving Young's modulus [Pa] as a function of the temperature field T. // This internally uses a natural cubic spline interpolation of the loaded data samples. expression E(measureddata, T); // nu is Poisson's ratio []. double nu = 0.3; // Define an arbitrary space-dependent temperature field for illustration: T.setvalue(vol, 473+100*(1+x)*(1+y)); formulation elasticity; // The linear elasticity formulation is classical and thus predefined: elasticity += integral(vol, predefinedelasticity(dof(u), tf(u), E, nu)); // Add a volumic force in the -z direction: elasticity += integral(vol, array1x3(0,0,-10)*tf(u)); elasticity.generate(); vec solu = solve(elasticity.A(), elasticity.b()); // Transfer the data from the solution vector to the u field: u.setdata(vol, solu); // Write the deflection to ParaView .vtk format with an order 2 interpolation: u.write(vol, "u.vtk", 2); // Write Young's modulus in space for illustration: E.write(vol, "E.vtk", 2); // Print the peak deflection: double umax = norm(u).max(vol,5)[0]; std::cout << umax << std::endl; // Code validation line. Can be removed. std::cout << (umax < 9.63876e-10 && umax > 9.63874e-10); } int main(void) { SlepcInitialize(0,{},0,0); sparselizard(); SlepcFinalize(); return 0; }
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